Steady Vs Unsteady flow over a cylinder
JORGE LOZANO
Advanced CFD using ANSYS Fluent
Steady Vs Transient flow over a cylinder
This article shows the flow characteristic of a laminar a flow at 10, 100, 1000, 10000, 100000 Reynolds number. The simulations were performed by solving the steady and transient 2D: Navier-Stokes equation for the 100 Reynolds simulation and the other with only the steady state, applying the SIMPLE and PISO algorithms. The drag and lift coefficient (Cd and Cl) as well as the Strouhal number were obtained and verified to the previous studies..
Objective
Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.
- PART-I: Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
- PART-II: Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Run with steady solver)
Discuss the effect of Reynolds number on the coefficient of drag. [ Results should be validated with any standard literature and error should be within 5 %]
Expected results:
- In both approaches, show that the flow has converged. That is, what quantities or plots need to be looked at to determine that the flow has converged?
- Plots of the coefficient of drag and lift.
- Plots to show vortex shedding behind the cylinder.
- Mention the preferred material at the end of the challenge submission page.
Strouhal number
The Strouhal Number is a dimensionless value useful for analyzing oscillating unsteady fluid flow dynamics problems.
The Strouhal Number can be expressed as:
St = ω * l / v
where
- St = Strouhal Number
- ω = oscillation frequency
- l = characteristic length
- v = flow velocity
The Strouhal Number can be important when analyzing unsteady, oscillating flow problems. The Strouhal Number represents a measure of the ratio of the inertial forces due to the unsteadiness of the flow or local acceleration to the inertial forces due to changes in velocity from one point to another in the flow field. F.1 shows an analyzed data results testing along several surfaces at a variation of reynolds number.
F.1 Stouhal number vs. Reynolds number plot
SIMULATION SET-UP
To perform simulations using Ansys/Fluent it’s desirable to have knowledge in the type of fluid model to adjust the condition of turbulent or laminar models according to the Reynolds number, the naiver-stokes equations, mesh characteristics, and the data postprocessing. For this case several simulations will be performed variating in the mesh, and initial conditions having as follows parametric results, duplicating several simulations and modifying the unique variables, as in F.2.
F.2 Project schematic
CAD Design geometry
The geometry consists of a simple circle being around a 2D surface of 60m of length,40 meters from the center in front of the circle and 10m above and below the circle, as follows in F.3, having a general mesh with 62,730 elements in tetrahedral form, revising the skewness quality, adjusting the name selections and the conditions to perform the mesh.
F.3 Set-up and Complete mesh
F.4 show the boundary layer thickness formula for exterior surfaces according to the known Reynolds number within the geometry, by which applying the larger total thickness of 0.25, along many divisions (10) to perform a fine and good boundary layer obtaining good precise results.
F.4 Inflation calculation and close-up
For convince of analytical calculation the material’s properties will be modified as to density as 1 and viscosity as 0.02 in the MKS system, applying the solutions reports, plots, animations, and files as follows in F.5, maintaining the convergence of the simulation and desirable post-processing conditions. The only inital condition that will be modified to obtain the reynolds number desired is the initial velocity, starting from 0.1 up to 1000 m/s over the same material properties and geometry, with the laminar method.
F.5 Material initial conditions and original conditions and solution setup
RESULTS
Several plots from each simulation will be presented from F.6 to F.15 showing the results for residuals, velocity vertex magnitude 8m directly behind the center of the geometry, drag and lift total coefficients and the Strouhal number along the Power Spectral Density out of the steady state and transient 100 Reynolds number systems. For all simulations besides the convergence results out of the Residuals plot, the velocity and lift coefficient plot must show a quasi-steady frequency plots, for which by having at least two wavelength we can determine the result range for which the min. and max. can be determine by the plot.
Steady state simulation
F.6 Steady state residuals, Re=100
F.7 Steady state vertex average of velocity magnitude, Re=100
F.8 Steady state drag coefficient, Re=100
F.9 Steady state lift coefficient, Re=100
F.10 Steady state Strouhal number along lift coefficient, Re=100
ANIMATION 1 VELOCITY CONTOUR
ANIMATION 2 PRESSURE CONTOUR
ANIMATION 3 VORTICITY CONTOUR
Transient simulation
F.11 Transient residuals, Re=100
F.12 Transient vertex average of velocity magnitude, Re=100
F.13 Transient drag coefficient, Re=100
F.14 Transient lift coefficient, Re=100
F.15 Transient Strouhal number along lift coefficient, Re=100, (X-axis 1E^1)
ANIMATION 4 VELOCITY CONTOUR
ANIMATION 5 PRESSURE CONTOUR
RE 10
F.16 Steady state residuals, Re=10
F.17 Steady state vertex average of velocity magnitude, Re=10
F.18 Steady state drag coefficient, Re=10
F.19 Steady state lift coefficient, Re=10
CONTOUR 1 VELOCITY
CONTOUR 2 PRESSURE
RE-1000
F.20 Steady state residuals, Re=1000
F.21 Steady state vertex average of velocity magnitude, Re=1000
F.22 Steady state drag coefficient, Re=1000
F.23 Steady state lift coefficient, Re=1000
CONTOUR 3 VELOCITY
CONTOUR 4 PRESSURE
RE-10000
F.24 Steady state residuals, Re=10000
F.25 Steady state lift coefficient, Re=10000
F.26 Steady state drag coefficient, Re=10000
F.27 Steady state vertex average of velocity magnitude, Re=10000
CONTOUR 5 VELOCITY
CONTOUR 6 PRESSURE
RE-100000
F.28 Steady state residuals, Re=100000
F.29 Steady state vertex average of velocity magnitude, Re=100000
F.30 Steady state drag coefficient, Re=100000
F.31 Steady state lift coefficient, Re=100000
CONTOUR 7 VELOCITY
CONTOUR 8 PRESSURE
CONCLUSION
By having simulated a system with a steady state and transient methods, analyzing a laminar flow, obtaining for each one of them their own significant convergence according to the velocity, drag and lift coefficients to a quasi-steady results, the final (average) drag and lift coefficients were calculated for all of them as well as the Strouhal number for the 100 Reynolds calculation, getting close to the initial, experimental data for both steady and transient cases, meaning the precision and accuracy of the time steps and mesh performed, F.32 and F.33 show the table and graph results.
Due to oscillation aroung the cylinder the lift coefficient's range is around the positive and negative values (in a graph), resulting in a close to 0 result, although the maximin and minimum values obtain in the graphs are important, they will define wherer or not the geometry will be affected structurally, meaning that the velocity shown is apprearing to obtain the vortex shedding behind the cylinder.
Contours and plots were post-processed in order to facilitate the selection and determine the variations within the independent variables. One of the characteristics of the velocity and pressure contours above the 1000 Reynolds number is the chaotic values for which the range may have very wide values and it's important to know the vorticity perfromance and the velocity in which it happens to obtain a good visualization in countours and animations.
F.32 Complete table results
F.33 Graph approximation, own results vs. [3] Article results.
One important fact to mention is the material preferred in experimental analysis, and the truth is that it really depends on the size, velocity and the Reynolds number desired, as seen in the graphs and articles mentioned all have several sizes for each Reynolds number, from a millimetre up to meters of diameter being applied several velocities to cover a well defined and measured data, at a laboratory usually the fluid which can be controlled and analyzed better is water at a certain temperature to vary its properties.
At F.34 the image shows one of the many natural examples over the clouds, image taken from the NASA earth observatory, showing the velocity oscillation, and vortices generated, seen that any fluid just by varying its size can be analyzed.
F.34 [4] Alternating vortices in the clouds on the lee side of Tristan da Cunha, a volcanic island in the South Atlantic.
The following link will contain the ANSYS WORKBENCH simulated data:https://drive.google.com/file/d/1n2LIBFNkNHNCJZq6YTSzCuaAh3220aSe/view?usp=sharing
REFERENCES
- Numerical simulation of laminar flow past a circular cylinder, Authors: B.N. Rajani, A. Kandasamy, Sekhar Majumdar, Science direct article. 2 February 2008
- https://www.engineeringtoolbox.com/strouhal-number-d_582.html
- Aerodynamic Drag Characteristics and Shape Design of a Radar Antenna Used for Airport Ground Traffic Control, Baris Gumusel , Levent Kavurmacioglu and Cengiz Camc, March 2, 2006, ISROMAC.
- Periodic Flow Motion – The Strouhal Number, Nikolaos D. Katopodes, in Free-Surface Flow, 2019
- https://www.sciencedirect.com/topics/engineering/strouhal-number